On the re-emergence of motion and innovations in the Gábor Bódy's intermedia experiments

The article explores the main cases of Hungarian neo-avant-garde cinema in terms of re-emergence of visual material and the introduction of electronic innovations resulting in the transformation of reality. Among the research conducted in Béla Balázs Studio based on reframing the perception limits in the 1960s and the 1970s, the most innovative were Gábor Bódy's intermedia experiments. Along with launching K/3 subgroup within BBS, Bódy directed its objectives to reduce the material derived from reality and to visually intervene into media image electronically transforming the landscape of his films. Innovatively adapting the Sándor Weöres's verse, the film Narcissus and Psyche (1983) aimed at using hyper-real aesthetics to reframe the film reality. Starting from 1980, Bódy founded an international magazine Infermental to disseminate the advent of the video and electronics by creating a community drew on sharing news about emerging media image.

In his essay on the poetics of experimental and documentary cinema in the 1970s, Lóránt Stőhr claims that the specific features of these experiments focused on the transformation of reality from different angles and began a new phase of visual research pioneering in the human sciences. 1 These years of Kádár-Era Hungary were marked by the re-emergence of the hybrid forms of Hungarian neo-avant-garde cinema. The entire period framing the ''Kádár regime'' encompassed 33 years, between 1956 and 1989, although these three decades ceased to form one coherent period, as the boundary context marks the years 1958 as a ''Kádárite consolidation'' tied with his version of state socialism and 1973 as a suspension of economic reform. As John Cunningham argued, ''after 1948 any avant-garde or even mildly experimental work was viewed with suspicion or vilified as bourgeois and decadent, and if any such work was carried out it was kept quiet.'' 2 Despite political setbacks, during the post-56 era, it started to emerge as an experimental neo-avant-garde, particularly at the Béla Balázs Studio (BBS) devoted to the exploration of image and visual language in multifarious manners. BBS was particularly the source of experimental films in Hungary, providing facilities and discursive space not only to most artists but also for publishing videocassette magazines such as Black Box and Infermental. From the outset of 1970s, the artists created their own line of production of independent films reaching for the new solutions of image investigation. In particular, the front line of neo-avant-garde experimentalism was aligned with launching Film Language Series (1972Á1975) highly preoccupied with semiotics. Along with the foundation of K/3 Studio at the BBS, notable concepts and works combining theory with practice were created. This combination of theory and practice particularly motivated Dora Maurer's idea of consistent structuralism in Relative Vibrations (1972) and Triolo (1970); Janos Toth's inimitable technique, studies, and private wealth in Study I (1974) and Study II (1975); Agnes Hay's plasticine BBS animation in Gyurma (1972) and Ü ldözés (1975); or Gábor Bó dy's wide range of visual works. The complement of this part of the neo-avant-garde was films made by artists usually dealing with other arts. Among them, it is worth mentioning the works prepared in the BBS such as Self Fashion Show (1976) by Tibor Hajas taking the subject of passersby in the streets of Budapest or Dream Reconstruction (1977) by Mikló s Erdély's examining perceptual relations between real-life, dreams, and the cinema. Thereby, BBS from the 1970s seemed to blur the boundaries between the genres of film, media, and art paving the way for new experiments in the area of intersections of media image.
The most innovative and prolific among these prominent figures of these years seemed to be Gábor Bó dy, who in 1971 joined the prestigious BBS that was devoted to the formal aspects of visual sphere already established in 1958 Referring to the origins of the outlined topic, after the main reorganization of the studio in 1960, the program of the studio seemed to be unprecedented in Europe. One of the reasons for the uniqueness of the BBS was the fact that independent filmmakers could accept or reject the subject of the proposed production, whereas the director was not entitled to take remuneration because the budget was at his disposal only for directing the film. Unlike the dominant ''engaged'' cinema focused on the political and social topics, politically involved cinema identified with the works of Zoltán Fábry, István Gaál, Mikló s Jancsó, András Kovács, Károly Makk, and István Szabó had already gained international acclaim. 3 The new generation of experimental artists selected the use of various heterogenic materials as a starting point of their experiments. The experimental filmmakers were focused on the exploration of the image realm of the form itself. Along with the foundation of BBS, composed of members from the world of fine arts, music, and film, a space has been created for students to perform experiments, try out new ideas, and explore innovative techniques and new modes of filmmaking. In particular, BBS has been focused on the preparation of sociological documentaries drawing on shooting practice into the research of reality. Conversely, it has been organized to help develop the young generation and open up new opportunities for them. 4 This experimental institution composed of graduates of the Academy of Theatre and Film and Philosophy and was partly supported by the Ministry of Film. Therefore, in 1972Á1975, the studio could have focused on exploring the relation between film language and linguistics within the framework of ''Film Language Series.'' István Nemskü rty argued that this group aimed to produce films that served as a prism through which the filmmakers expressed their views on the world in which they lived and worked. 5 By arguing to abandon the common ''topo-chronological system of narrative,'' Gábor Bó dy's circle was highly preoccupied with various forms of serialism as a form that could reflect new modes of narrative. 6 Among numerous theoretical concepts drawn from the idea of correspodances des arts, the most K. Lipiński challenging seemed to be the theory of aleatory accident based on the underlying premises of serialism. By working across disciplines such as visual arts and linguistics, Bó dy's research was immersed in the theory of chance based on ''the idea of aleatory dodecaphonic language of the film movement.'' 7 In other words, the theory of chance was considered to be an indispensable element of every filmic and electronic intervention into narrative modes.
This predilection to the examination of medium reflects some parallels with other European intermedia pioneers from the end of the 1960s and at the beginning of the 1970s. This time of transition characterizes the experimental period of Jean-Luc Godard who was working with Jean-Paul Gorin within the Dziga Vertov Group (1968Á1972) and with Anne-Marie Miéville within the Sonimage project (1973Á1979). The main aim in both projects was to explore the nature and various interconnections between a moving image and the static photography, raising the issue of the status of the medium itself. In parallel, it has been established in Lodz peculiar in Central Europe and unique in Poland progressive Workshop of Film Form (Warsztat Formy Filmowej, 1970Á1977). The main representatives and founders were Wojciech Bruszewski, Paweł Kwiek, Jó zef Robakowski, Andrzej Różycki, Zbigniew Rybczyń ski, Ryszard Waśko. The main purpose of this group was to concentrate on the analytical approach to the audiovisual film form investigating it in terms of a wide range of issues such as construction of space, time, and plasticity and the reference to reality. Gábor Bó dy was probably the most close to the Polish group, with whom he shared parallel structuralÁ analytical interests and was a friend of Jó zef Robakowski and Małgorzata Potocka. Likewise, Godard and the Workshop of Film Form, Bó dy's works, took a place between cinema and contemporary art, and shared the similar ideas of independent production and its autonomy, placing cinema as well as the predilection to self-reflexivity of medium to explore the relation between the image and the viewer.

INNOVATIONS WITHIN K/3
The result of founding the separate section K/3 group in 1973 within BBS was the creation of the platform for experiments that reshaped the postwar Hungarian avant-garde film's path. The main purpose of this research was to impose a specific point of view on the reality and to intervene and affectively modify the life of the public. 8 As Miklós Péternak points out, ''K/3 was established with the ambition of becoming a Bauhaus-like center for research in the audiovisual area.'' 9 From the outset, the K/3 subgroup was established as a Complex of Cultural Research, including Miklós Erdély, Zoltán Jeney, Dó ra Maurer, László Vidovszky, Endre Tó t, Tamás Szentjó b, and Á kos Birkás who were focused on the exploration of intersections between cinema language and signification. As Lorad Stő hr argues, the proposed reflections on reality sought to recapture the motion and to unveil the essential characteristics of reality, thereby discovering the viewer himself. The second purpose of the cluster was to emphasize the importance of distribution of documentaries to reach out to a wider audience of the public, thereby arousing interest in a particular social problem, stimulating discussion and mutual reflections. 10 In light of the basic assumptions of the group, the ontological purpose of the documentary was not to reflect the reality itself, but to present a moving image as the complex object of transformation relying upon the ''reduction of material derived from reality.'' 11 This form of ''miniaturized film factory'' was intended to complete the specific function of public education and to serve as the open space for the freedom of experiment. 12 The reasons for these feelings were manifold. One example of formally exploring the freedom to experiment was the desire to present from different angles of various stages of dance in the documentary Four Baggatelles (1975). 13 This movie has applied paradoxical strategy of incrustation of an image based on an increasing alternation of internal frames within the frame exceeding semantic conventions and overlapping narrative sequences. Merging the image from various perspectives brought about blurring of the borderline of filmic reference and questioned the formal aspects of pictorial tradition.

COMPUTER AND MOTION
Drawing on the use of formal techniques, the strategy of a re-emergent image evolved progressively from the first use of computer film in Hungary. Previous work experience at the Hungarian television and film school enabled Gábor

Re-emergence of phases in motion
Body to create the specific model of intermedia motion in Psychokosmen (1976). These ideas were strictly generated by computer algorithm, as the psychotechnical form of the script, which represented documentary stages of motion based on the continuous quoting of one excerpt Cosmic eyes. The main reason of this fragmentary quoting was the fact that BBS had submitted a screenplay (1975) for this film that was ultimately filmed but not completed. Therefore, the signals transmitted by the computer simulator produced images harmonizing with certain parameters. 14 The specific idea of screenwriting drew on the assumption that radio, as a device joining continuous signals, has the ability to locate it within one source and place. As Patérnak argued, the experiment has shown that a man is unable to draw random lines in a spontaneous way. Devoting to draw them for a substantial period of time, the ''Kostruction'' was based on forming and conducting experiments in 15Á20 steps. Specifically, the algorithm produced ''continuous, irregular lines'' dispelling ''the construction of many correct versions,'' which have become ''the error in limiting case of random.'' 15 Used in this experiment, a fortuitous movement played the role of a trigger looking ''much more real'' and enforcing ''rules with human effort.'' 16 Therefore, an inadvertent movement stimulated the ''moving diagram depicting the tensions of a psychic space'' in which the quality of elements was variable. What characterized the main strategy of this movement used in the diagrams was emphasizing the ''significance of spatial arrangement.'' 17 It should be noted that his approach to recurrent experimentalism was marked by the experimental transition to his first full-length film Amerikai Anzix (American Postcard, 1976) based on the use of the formal solutions already applied in his short films. 18 In this movie, Bö dy used strategies such as ''various acoustic and visual postproduction techniques dissecting his images into elements.'' 19 By reconstructing historical settings, the film depicted a search for American Dream, particularly recapturing the lives of Hungarian 1848 Revolution veterans in the American Civil War based on a method marked as ''light editing,'' which alluded to the silent film. In a similar manner, Bö dy was preoccupied with historical research in the documentary Private History (Privát történelem, 1978) in which he selected a compilation of sequences collected and derived from home movies from the inter-war period. Drawing on amateur movies derived from the original context of personal recordings, Bó dy focused on the specific techniques of blow-ups and inserts using freeze-framing, slow-motion repetitions, and screen splitting. Unlike André Bazin's theory of mummification of images, these techniques followed the years that have re-emerged on the screen and revealed the desired fiction as the flipside of an image projected for the audience.

LANDSCAPES OF ABJECT AND TRANSGRESSION
The crucial characteristics of his most well-known feature film was a theme of migration embedded in the context of poetics of openness drawn on Sándor Wérö es's verse drama in his largest scale epic fiction of its era Narcisz és Psyché (1980). A gigantic production budget embraced a course of a historical period presented in richly designed decors and costumes starring Patricia Adriani, Udo Kier, and Gyö rgy Cserhalmi, whereas the main characters such as Laci Toth and É rszebet Lonyai represented Psyche and Narcissus. This national super-production has been distributed in three different versions: one circulating as an original lasting 210 min, a two-part version devoted to foreign screenings with the first part running 136 min and the second 270 min, and a three-part television version described by the commentators as an ''escalating intervention.'' 20 By taking the theme of transnational migration, the movie was abounded in the ''baroque fireworks of associations,'' which oscillated ''between a high degree of stylization and the conscious use of 'kitsch', uplifted by the use of ironic quotation or electronically transformed music.'' 21 The most striking effect of these transformations was the so-called bio-radicalism, a term introduced by Gábor Bachman that spanned various expressive representations of embodiment. Namely, a woman personifying Psyché played the role of a decadent figure that was eager to often play with social taboos. It represented a particular lifestyle and a search for the escape from boredom through the pleasure of sexual relationships. This woman figure could be considered by Julia Kristeva as a symptom of ''absurdity, stupidity, violence, sorrow, moral and physical degeneracy,'' which are interpreted K. Lipiński by her as the form ''formal fashion, in that interspace between abjection and fascination.'' 22 Standing for a symptom of decadency, this particular lifestyle identified with Psyché ''tackled with fascination if not with a certain amount of sympathy, that we are presented with a wild, obscene, and threatening [. . .] an image of downfall, abject poverty.'' 23 The most frightening among several explicit scenes was one that illustrated the operation of the removal of a polyp from the body of the main figure Psyché. The polyp removal operation can be interpreted as a figure of abject as negation and its three modalities: transgression, denial, and repudiation of the viewer. 24 The red polyp stands for a violent, repulsive object considered by Kristeva as a ''symptom of ego that, overtaxed by a 'bad object', turns away from it, cleanses itself, and vomits it.'' 25 This repulsive object presented in the form of the polyp can be defined as ''one of those violent, obscure revolts of being, directed against a threat that seems to emanate from an exorbitant outside or inside.'' 26 The rejection of an obscene polyp manifests itself in ''corporeal waste, menstrual blood and excrement, or everything that is assimilated to them, [. . .], represent-like metaphor that would have become incarnate*the objective frailty of symbolic order.'' 27 Symptomatic fixation of the camera in the long-lasting close-up on the bloody red polyp in the foreground stands for ''a sign of 'jouissance' unveiling in this new light that what was already repressed.'' 28 Setting the camera on one single object in this long-lasting freeze-frame tended to exceed the ''symbolic order.'' Kristeva particularly argued that this form of transgression is ''assured as soon as there are images which secure unfailing belief, for belief is in itself the image: both arise out of the same procedures and through the same terms: memory, sight, and love.'' 29 The fixation of the camera resulted in these triple modalities of abject, which occurs in Kristevian terms when ''separation between subject and object is not yet clear but where these two quasi entities are exhausted in fascination and repulsion.'' 30 In this sense, ''this 'site of maximum abjection', as Jacqueline Rose stressed, is placed where the 'savagery' of the speaking being can be heard [. . .] taking shift to subjectivity and the unconscious at its word (body and letter) through a clinical engagement with acquisition, dissolution, and pathology of language, all of which had laid beneath the earlier analysis of literary form and style.'' 31 Kristeva argued that the long-lasting representation of the polyp seemed to reflect the ''pathology that was in danger of being restricted to its aesthetic mode. 32 In this view, the subject seeks to save this idealization from the tyranny of the symbolic, in which ideals are shaped.'' 33 The vision of bloody polyp is characterized by tyranny of symbol, which Kristeva describes as a ''celebration of the semiotic to abjection and back to a (now paternal) ideal the instability of fantasy itself.'' 34 In Kristevian terms, the dead polyp could be considered as the death of the sign as well as the death of idealization in our culture. The symbolic meaning of this transgressive scene reflects Christopher Lash's claim, according to which ''death precipitates an abolition of psychic space and let the abjection to reign.'' 35 However, the purification of the polyp brought about that Psyché recovered and subsequently decided to leave the country. In the face of the threat of outbreak of World War I, after the return to Silesian, she traveled with nobleman Zedlitz to Brazil and subsequently decided to emigrate to the United States. By traveling in the waves of emigration, Psyché confirmed Kristevian's claim, according to which ''Imaginary such as crossing national boundaries can serve as'' antidote to the crisis. 36 As Péter Gyó rgy pointed out, Narcissus and Psyche (1981) was a fruit of ''a very forceful reaction to both the legacy of abstract, insensible Conceptualism and the sad moral vacuum of everyday of Hungarian life.'' 37 The carnivalesque ambiance of ambivalent love stemmed from the conceptual vision designed by István Hildebrad. The scenery was enriched with ''filters and screen, lamps and specially polished with colored lenses'' advocating the advent of an electronic era. 38 Particularly, Gábor Bachman prepared the pre-stylization of a film in the settings of surrealist scenery. The vibrant colors rendered the ''New Sensibility'' of the era and represented the break with traditional storytelling in an extremely radical way. 39 Unlike the artistic strategies used within the realistic paradigm, the ''engaged'' modern representation of socialist life was based on the use of a wide array of such complex embellishments. Specific modification of image reality designed in the scene of a couple having love fixed in stop-motion caused blurring the relation between signifié and significant. A conceptual shift in hybrid deformation of documented phases of motion seems to be Re-emergence of phases in motion observable in complex exposure of gathering objects of performances, which occurred in the final scene in the Palace. Namely, the scene of human figures forming together the composition of various geometrical axes was continued by the denudation of the whole public. An eccentric landscape of these acts of ''openness'' can be considered in Giorgio Agamben's terms as a ''ruthless denudation of the body with all the signs of its sexuality, which become visible for the eyes that had now been 'opened' by sin, can only be understood if we presuppose that what was 'covered', that what was before veiled and dressed is now unveiled and undressed.'' 40 Unexpected climax of the visual sphere played the role of a dominant moral vacuum in socialist culture representing not an abject, but an object based on the geometric grid of hybrid forms. The human figures were presented as both the elements of settings and the precise element of the study. The use of electronic techniques of hyperstylized reality entailed specific embellishments composed of not only formal aspects of an image but also transforming Martin Jay's ''scopic regimes'' of modernism. The final scene showing Narcissus and Psyché embracing can be interpreted as a interstitial zone of abject expressed explicitly in Kristevian's claim, according to which '''modernity' has learned to repress, dodge, and fake.'' 41

RE-EMERGENCE OF THE PHASES IN MOTION
Although the outset of playful random lines extends beyond aesthetic regimes of modernism, at times it relates to the legacy of modernism. This context can be witnessed in motion studies such as Homage to Eadweard Muybridge 1880Á1980 that drew on the Muybridgian pre-stylization of live recordings showing various stages of body movement. Electronically deformed effects investigated the gradual phases of the movement of human figures seen in stop-motion. It shows the re-emergence of the ''supplementary element'' presented in the form of deformation stemmed from the framework of analysis in Psychokosmen. 42 This homage to Muybridge's oeuvre presented one precise element of body images perceived in the form of continuous sequence of narrative. One of the examples illustrating the effects of hybridization of arts was a scene based on interspersing the narrative with the grid of vertical and horizontal lines. It introduced the human body as an object of the study of the movement stimulating visual effects generated by the computer as the examples of experimental tendencies in the early 1980s. This electronic transition has been emphasized by the advent of artificial intelligence introducing the post-synchronic voice of narrator stylized as the speech of a robot in the foreground. One of the reasons for oncoming new forms of representation of the 1980s was the introduction of an innovative aesthetics of video-clips described by Laurent Jullier. The new aesthetics heralded reframing modern ''ways of seeing'' characterized by the three shorts enmeshed in the literary and philosophical contexts. In light of this, Bó dy shows triple cycle in shorts such as De Occulta Philosophia (1981) and Dance of Eurynome (1983) representing philosophical contexts, and Walzer (1985) drawing certain literary inspirations from mythological themes. In a closer look, De Occulta Philosophia (1981) unravels its focus on the visual translation, which finds its reflection in the Agrippa of Nettesheim's symbolism and the transformation of numbers into images. It confronts both formal underlying premises of film narrative with philosophical and mythical themes. The latter themes in De Occulta Philosophia (1981) presented the image of visualized knowledge as the reminiscence on Occultism reflecting the nature of man drew on the direct associations with the Renaissance and Leonardo da Vinci, the treatise of Agrippa reworking a disassociating geometry. In this project, Bó dy transformed the symbols within the framework of numbers, thus heralding the advent of the database paradigm by Lev Manovitch and Peter Greenaway's haunting visual obsessions. The next step in the development of the intermedia theory was the production of short entitled Dance of Euronyme composed of six various tapes saturated with the visions of monitors and sound tracks. In accordance with an aesthetic of video-clips characterized by the elaboration of electronic dimensions of visual codes, these shorts paved the way to show the role of the human in electronic space. The last part of the trilogy was Waltzer (1985) devoted to the illustration of translation of Novalis's s literary poetry into visual sphere. Consequently, all three Body's video works examined the symbols for the origins of life, the laws and principles seen in the perspective of anthropocentric world view, as well as presenting the entire cycle as coming into being and to an end.
Interestingly, Bó dy's final film Dog's Night Song (Kutya éji dala, 1984) was based on the recurrent use of the strategy of home footage, previously explored in the experimental film Private Hungary (1978). Unlike the previous project, in this film Bó dy focused on the idea of persecution fight, casting himself and incorporating such amateur techniques as the use of Super 8 and video footage. The purpose of the project was to reframe a wide range of emerging Hungarian underground concerts of contemporary punk bands, which mirrored the specificity of emergence of new social movements. A wide variety of experimental gestures imbued the narrative structure of The Dog's Night Song imposing visual layers on medieval iconography. Via using such innovative recording techniques as different filters and lightening, Dog's Night Song showed certain image transformation devoted to stylization of reality in documentaries. Specifically, Bó dy imitated newsreel stylization as a result of the cutting and fracturing the prefilm facture that appeared previously in the torn postcards of American Postcard. 43 The use of the strategy of re-emergence of previously used material contributed to the fact, as Bálint Kovács argued, that the film gave an impression of being ''undisciplined and chaotic.'' 44

FOUNDATION OF INTERNATIONAL NETWORK
In exploring new directions of circulation of forms, Gábor Bó dy directed its objectives to reshape the framework of international community based on organizing a network composed of contemporary video artists. As the starting point, this international cooperation was the foundation of the magazine entitled Infermental, launched in 1980, and was devoted to the publishing of videocassettes. The project progressively gained international acclaim and reached wide distribution. According to Gábor and Vera Bó dy, the main purpose of the project was to seek ''the heterogeneous, process-based and collective currents in the media sector'' that presented their ''counter hegemonial ambitions.'' 45 The first issue of ''Infermental'' was published in Berlin in 1982 as the first international videocassette magazine coedited by Astrid Heibach and Gábor Bódy. It presented video artworks partly or entirely composed of trailers and reports lasting from 1 to 20 min from around the world, which were promoted on a massive electronic billboard during the Berlin Film Festival. Each issue was compiled and edited in a different worldwide location and published annually with a total running time between 4 and 6 h. The magazine, composed of 660 works gathered together in the last issue, was published in Skopje and Osnabrü ck in 1991. Not without a reason Oliver Hirschbiegel called this magazine a ''running information memory,'' as it joined together excerpts, documents, and events organized in terms of ''thematic and intellectual context.'' 46 Until disbanding the project in 1991, this information store was compiled annually from different periodicals made up of visual footage. In particular, the videocassette was perceived as an ideal circulatory medium that could replace deploying the littleused and expensive laser disks, which facilitated access and playback of discs. 47 Innovative laser beams structured the duration of the tape and triggered the collaboration with Llurex led by Egon Bunne at the DFFB in Berlin. Both Infermental and Llured Network complemented with a unique archive of the trends, theories, images, and movements of the 1980s provided, according to Rudolf Frieling, ''an insight into the topology of the media directions.'' 48 This project was based on the idea of international unity and cooperation faced and decontextualized preexistent conventions, providing innovative transpositions of contexts, which allowed the emergence of new artistic visions in the journal of international scope.
In light of what has been discussed before, it is not at all surprising that with these intersections between techniques of image manipulation and linguistics, the works and projects launched by Gábor Bó dy acquired a memorable place in the history of intermedia studies bridging the past with present. This re-emergence of image media was following Jonathan Crary's statement, according to which ''modernization entailed a decoding and modernization of vision.'' 49 The initial period of circulation of ideas in the 1970s resulted in the advent of electronic devices that transformed the role of the image itself. Using the strategy alternation, the frame within the frame heralded the advent of ''post-photographic'' era, as W.J.T Mitchell declared, characterized by emerging postproduction image manipulations that blurred the relations Re-emergence of phases in motion between significant and signifié questioning the articulation of modern paradigm. Finally, one might say that this re-modernization of vision based on the re-emergence of flamboyant visual effects proved to be ''a condition of possibility'' both for the artistic experimentation of modernism and for new forms of domination, for what Foucault calls the ''technology of individuals.'' 50 Notes


extfieldsofstudy: Philosophy Mathematics

text:
Comment on Article by Berger, Bernardo, and Sun

Discussion of Overall Objective Priors by James O. Berger, Jose M. Bernardo, Dongchu Sun [arXiv:1504.02689].

Introduction
The search of a prior distribution p(ω) to be used as part of an objective Bayesian analysis of a model p(x|ω) has proved to be a formidable endeavour. This is an area where we do not have a definitive answer yet, and any contribution to the understanding of the subject must be welcome. The authors of this paper are among the most prominent contributors to this field, and reading the manuscript has been very stimulating.
Research on the problem has mainly dealt with three issues: first, a definition of what a non-informative, reference or objective prior p(ω) must be; second, an operational algorithm to calculate such priors; third, the evaluation of the resulting prior(s) in accordance to certain criteria such as invariance, the avoidance of paradoxes, or desirable frequentist properties.
To us, and this is a subjective judgment, the most convincing approach to produce this sort of priors is reference analysis (Bernardo, 1979;Berger and Bernardo, 1992a,b;Bernardo, 2005;Berger et al., 2009). This procedure: (i) defines the reference prior as the prior maximizing the expected gain of information provided by a sample; (ii) includes a general (although potentially involved) algorithm to calculate the prior; and (iii) avoids a number of paradoxes. Moreover, it generalizes the Jeffreys prior and exhibits its limitations. Among its most remarkable results, it shows that the form of the reference prior p(ω) may depend on the function of the parameters θ = θ(ω) which is considered by the researcher to be of main interest.
Since its inception, the algorithm to obtain reference priors has evolved. This is the case specifically in the multiparameter setting. The most recent version (Berger and Bernardo, 1992a,b) requires all scalar components of the parameter to be strictly ordered in terms of their inferential interest. Thus, in principle, the current approach does not offer any solution if the researcher is simultaneously interested in two or more scalar parameters (or functions thereof). Interestingly, the original algorithm of Bernardo (1979) did cover this situation, although the solution was the multivariate Jeffreys prior which leads to unsettling paradoxes in some cases.
In this paper, the authors explore some ideas to extend the reference analysis to this yet unsolved case. They also seem to be considering a more general version of the problem by assuming that the number of scalar parameters (or functions of the parameters) of interest may be greater than the number of parameters in the model. So, the question is: What should the objective prior π R (ω) (ω ∈ R k ) be if there are m functions (θ 1 (ω), θ 2 (ω), . . . , θ m (ω)) which are of simultaneous interest, where m is not constrained to be less than or equal to k? Three methods to produce the required prior distribution are discussed: (i) the common reference prior; (ii) the reference distance approach; and (iii) the hierarchical approach.

Common reference prior
This is not really a method. If the reference priors corresponding to θ i (ω) as the parameter of interest (i = 1, . . . , m) are the same for any ordering of the remaining parameters, then the posed problem simply vanishes. It is interesting to see some examples illustrating particular cases where the common prior exists, but it is desirable -and would be much more useful -to have general results characterizing sampling models where, for example, Theorem 2.1 applies and hence a common reference prior may be found. In this regard, results such as those in Gutiérrez-Peña and Rueda (2003) and Consonni et al. (2004) could provide a good starting point. These authors find reference priors for wide classes of exponential families that include the family discussed in Section 2.1.3 of the present paper as a particular case.
It must be pointed out that this section relies on the analysis of the information matrix I(θ), so all reviewed scenarios assume m ≤ k. Also, a somewhat disquieting result is that of Section 2.2.2, where the authors show that π R (ψ 1 , ψ 2 , ψ 3 , µ 1 , µ 2 ) ∝ (ψ 1 ψ 2 ) −1 is the one-at-a-time reference prior for any of these parameters and any possible ordering. In particular, it is the reference prior for the case where µ 2 is the parameter of main interest. It so happens, however, that this prior is equivalent to the right-Haar prior which leads to a problematic posterior precisely for µ 2 . This result would imply that, in general, reference analysis might produce inadequate posteriors for the parameter of interest, depending on the specific accompanying parameters.

Reference distance method
In order to introduce this method, the authors explicitly assume that θ = ω, hence m = k. The idea is to find an overall prior π(θ) such that each of its marginal posteriors π(θ i |x) is close to the corresponding marginal posterior π i (θ i |x) obtained when θ i is the parameter of interest (i = 1, . . . , m). As a measure of approximation the authors propose a weighted average of expected logarithmic divergences, although other measures could in principle be used. Also, the search for the overall prior is restricted to a specific parametric family F = {π(θ|a), a ∈ A}. Apart from the fact (acknowledged by the authors) that the existence of an optimal a is not guaranteed, a rather unappealing feature of this proposal is its dependence on the family F . The authors offer no guidance on how to choose F in general. If the aim is to produce an objective approach, it seems desirable that F be somehow intrinsic to the sampling model. The examples in the paper suggest that perhaps this could be achieved through some kind of conjugacy.
Incidentally, the reference distance method bears some resemblance to the meanfield approach to variational inference, which is relatively straightforward in the case of exponential families with conjugate priors; see, for example, Bishop (2006, Chapter 10). What is the authors' take on this?
We would like now to comment on Example 3.2.4. There, the normal model N (x|µ, σ) is considered, and the parameters of interest are µ, σ and φ = µ/σ. (Note that, despite the authors' remark at the beginning of Section 3, here θ = ω and m > k.) In any case, the authors remind us that the reference prior when µ or σ is the parameter of interest is π(µ, σ) = σ −1 , whereas the reference prior for φ = µ/σ is given by π φ (µ, σ) = (2σ 2 + µ 2 ) −1/2 σ −1 . They then propose, as a "natural" choice, the class of relatively invariant priors F = {π(µ, σ) = σ −a ; a > 0}. For this family, they show that the overall prior for (µ, σ, φ) can be approximated by π o (µ, σ) = σ −1 , so that inclusion of φ as an additional parameter of interest makes no difference. We find this rather disappointing. From an algorithmic point of view, this outcome is not surprising given the choice of F and the form of the reference priors for µ and σ. Only a large weight on the divergence corresponding to φ could lead to a different result. An idea that springs to mind is to try another (arguably more "natural" family) such as G = {π(µ, σ|a 1 , a 2 ) = (2σ 2 + µ 2 ) −a1 σ −a2 ; a 1 > 0, a 2 > 0}, which includes all three reference priors for µ, σ and φ. On the other hand, since π µ (µ, σ) and π σ (µ, σ) are equal in this case, the authors could alternatively have minimized the sum of the two divergences corresponding to the marginal posterior of φ and the joint posterior of (µ, σ)). We wonder how these alternative ideas compare with that proposed in the paper for this example.

Hierarchical approach
The idea of this approach is, first, to find a "natural" parametric family of proper priors π(θ|a) such that a ∈ R and the integrated likelihood results in a proper density p(x|a). Then, the univariate reference prior for a, π R (a), is obtained for this latter model. Finally, the overall prior π o (θ) is defined as the expectation of π(θ|a) with respect to π R (a). This is an intuitive and seemingly reasonable idea. However, it is not clear how to make explicit that θ is the parameter of interest even though the model is originally indexed by ω, especially when the dimension of θ is larger than that of ω. (See the comment below concerning the multi-normal means example.) We wonder if the authors can provide some advice on how this could be achieved in general. On the other hand, as in the reference distance case, dependence upon a specific family of priors introduces no small amount of arbitrariness in the method. Here, again, a proper objective method would use an intrinsic family entirely determined by the sampling model. One possibility, particularly suitable for the case of hierarchical models, would be to elaborate on the idea of conjugate likelihood distributions (George et al., 1993), although a suitable restriction should be imposed on the corresponding conjugate family in order to get a one-dimensional hyperparameter. Concerning the implementation of the method, the authors suggest that integration to get the overall prior can be avoided by using π o (θ) = π(θ|â) instead, whereâ is the mode of the posterior p(a|x). This proposal may be efficient from a computational point of view, but it is both surprising and disappointing since it essentially reduces the hierarchical approach to a standard empirical Bayes procedure and leads to a data-dependent prior.
The example in Section 4.2 concerning the multivariate hypergeometric model is confusing and does not quite illustrate the method described above. First, the parameters of the sampling model are given a multinomial prior (which does not depend on a single scalar parameter a, but on a vector of probabilities p k ); then, the likelihood is integrated and shown to yield a multinomial distribution. In the process, the k original parameters R 1 , R 2 , . . . , R k are replaced by the parameters p 1 , p 2 , . . . , p k , so the idea of reducing the problem to the determination of the reference prior for a scalar parameter is abandoned. Next, in the multinomial model, the approximate overall prior obtained using the reference distance method is adopted for the hyperparameters p k . Finally, the corresponding integrated Multinomial-Dirichlet distribution is declared as the overall prior for R 1 , R 2 , . . . , R k . We find this ad hoc combination of methods difficult to justify as a general procedure.
An alternative formulation could be based on the idea of super-populations (quite common in the field of survey sampling) as follows. Let us assume that a random sample of size N is obtained from a multinomial distribution M u k (Y k |1, p k ). As a result we get a vector R 1 , R 2 , . . . , R k describing the number of sampled units in each category. Now imagine that we then get a subsample of size n, without replacement, from the sample of size N . In this setting, the multinomial distribution describes an infinite super-population, the sample of size N is the finite population of interest and the subsample of size n is the actual sample we observe. Given the sample, the likelihood based on the subsample corresponds to that of a hypergeometric distribution. However, with respect to the super-population, the subsample is just a sample of the original multinomial population whose parameters are given by the vector p k . Within this framework, R 1 , R 2 , . . . , R k are observables and any inference regarding these quantities must be produced through the corresponding posterior predictive distribution. This argument shows that the hypergeometric problem can be viewed as a multinomial one where the interest is not really on the parameters but on observables, and the relevant overall prior is that for p k , no matter which method we use.
The example on the multi-normal means (Section 4.3) deserves a few words as well.
Here, the parameters of interest are, using the same notation as the authors, µ i ; i = 1, . . . , m and |µ| 2 = µ 2 1 + · · · + µ 2 m . First, we note that throughout the paper k refers to the dimension of ω and m is the number of parameters of interest (the dimension of θ), so in this example we have m = k + 1. It must be pointed out, however, that the hierarchical method, as defined, cannot be applied when m > k since the distribution π(θ|a) would then be defined over a space of functionally related components of θ and would be singular. This fact is implicitly recognized by the authors when they propose a prior for (µ 1 , . . . , µ m ) only, ignoring the last parameter of interest, |µ| 2 . They then argue that the resulting overall prior is reasonable not only for each mean µ i but also for |µ| 2 . The key issue here is the convenient choice of π(µ|a) as the product of the normals N (µ i |0, a). So, strictly speaking, this problem is not actually solved by using the hierarchical approach as proposed in the paper but by an ad hoc choice of π(µ|a).

Final remarks
This paper contains many interesting ideas and examples. However, it offers more of a brainstorming than a systematic treatment and a general solution to the problem. It is somewhat disappointing that the methods proposed in the paper bear little resemblance with the original reference prior approach, where the problem is clearly stated, the criterion used is sensible, and one can typically obtain unique and reasonable solutions. The approaches proposed here are still far from becoming operational algorithms since they require a number of arbitrary inputs. Hopefully, at least one of these methods will evolve into an overall objective procedure to find overall objective priors. We believe the reference distance method to be the most promising in this regard.